A fixed thermally conducting cylinder has a radius `R` and height `L_(0)`. The cylinder is open at its bottom and has a smaller hole at its top. A piston of mass `M` is held at a distance `L` from the top surface, as shown in the figure. The atmospheric pressure is `P_(0)`.

The piston is now pulled out slowly and held at a distance `2L` from the top. The pressure in the cylinder between its top and the piston will then be

Options

A. `rhog(L_(0) -H)^(2) + P_(0)(L_(0)-H) + L_(0)P_(0) = 0`
B. `rhog(L_(0) -H)^(2) - P_(0)(L_(0)-H) - L_(0)P_(0) = 0`
C. `rhog(L_(0) -H)^(2) + P_(0)(L_(0)-H) - L_(0)P_(0) = 0`
D. `rhog(L_(0) -H)^(2) - P_(0)(L_(0)-H) + L_(0)P_(0) = 0`

Answer

C

Explanation

Equating pressures
`P_(0) + rhog(L_(0) -H) = P = (P_(0)L_(0))/((L_(0) - H))`